[Numpy-discussion] Re: representation of valid float type range

Jan. 10, 2022

      Hello all.

I believe that over the years there were multiple proposals to replace the linspace formula start + n *(stop - start) / (npoints - 1) with a * start + b * end with a, b linearly spaced between 0 and 1 with npoints. Concretely, a = n / (npoints - 1), b = 1 - a. Here, 0 <= n < npoints.

I believe this would fix the issue here among many others. However, it was always rejected due to backward-incompatibility concerns. Perhaps it’s time to revisit this issue.

Best regards,
Hameer Abbasi
...
Am 10.01.2022 um 12:59 schrieb alejandro.giacometti@gmail.com:
I see what you mean, there is, however, some inconsistency on how this is handled, and it's not entirely intuitive
```
_type=np.int8
N=8
np.linspace(
   start=np.iinfo(_type).min,
   stop=np.iinfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([-128,  -92,  -56,  -19,   17,   54,   90,  127], dtype=int8)
_type=np.float16
np.linspace(
   start=np.finfo(_type).min,
   stop=np.finfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([-65504., -46784., -28080.,  -9360.,   9360.,  28080.,  46784.,
           65504.], dtype=float16)
_type=np.float32
np.linspace(
   start=np.finfo(_type).min,
   stop=np.finfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([-3.4028235e+38, -2.4305882e+38, -1.4583529e+38, -4.8611764e+37,
           4.8611764e+37,  1.4583529e+38,  2.4305882e+38,  3.4028235e+38],
         dtype=float32)
_type=np.float64
np.linspace(
   start=np.finfo(_type).min,
   stop=np.finfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([            nan,             inf,             inf,             inf,
                      inf,             inf,             inf, 1.79769313e+308])
_type=np.float64
np.linspace(
   start=0,
   stop=np.finfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([0.00000000e+000, 2.56813305e+307, 5.13626610e+307, 7.70439915e+307,
          1.02725322e+308, 1.28406652e+308, 1.54087983e+308, 1.79769313e+308])
_type=np.float64
np.linspace(
   start=-1e291,
   stop=np.finfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([-1.00000000e+291,  2.56813305e+307,  5.13626610e+307,
           7.70439915e+307,  1.02725322e+308,  1.28406652e+308,
           1.54087983e+308,  1.79769313e+308])
_type=np.float64
np.linspace(
   start=-1e292,
   stop=np.finfo(_type).max,
   num=N,
   dtype=_type,
)
=>    array([            nan,             inf,             inf,             inf,
                      inf,             inf,             inf, 1.79769313e+308])
_type=np.float16
np.logspace(
   start=np.finfo(_type).minexp,
   stop=np.finfo(_type).maxexp,
   num=N,
   dtype=_type,
   base=2,
)
=>    array([6.104e-05, 1.190e-03, 2.322e-02, 4.529e-01, 8.836e+00, 1.722e+02,
          3.360e+03,       inf], dtype=float16)
_type=np.float16
np.logspace(
   start=np.finfo(_type).minexp,
   stop=np.finfo(_type).maxexp,
   num=N,
   dtype=_type,
   base=2,
   endpoint=False,
)
=>    array([6.104e-05, 8.211e-04, 1.105e-02, 1.487e-01, 2.000e+00, 2.691e+01,
          3.620e+02, 4.872e+03], dtype=float16)
_type=np.float64
np.logspace(
   start=np.finfo(_type).minexp,
   stop=np.finfo(_type).maxexp,
   num=N,
   dtype=_type,
   base=2,
   endpoint=False,
)
=>    array([2.22507386e-308, 2.16653556e-231, 2.10953732e-154, 2.05403862e-077,
          2.00000000e+000, 1.94738306e+077, 1.89615038e+154, 1.84626556e+231])
```
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